Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator
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摘要
In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically.
论文关键词:Orthogonal spline collocation method,Nonlinear Schrödinger equation,Wave operator,Conserved quantity,Convergence,Stability
论文评审过程:Received 5 May 2010, Revised 10 September 2010, Available online 8 October 2010.
论文官网地址:https://doi.org/10.1016/j.cam.2010.09.025